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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception ---
 Ultimate Foundation of Truth
Date: Sun, 2 Mar 2025 10:02:16 -0600
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On 3/2/2025 9:23 AM, dbush wrote:
> On 3/1/2025 11:46 PM, olcott wrote:
>> On 3/1/2025 7:27 PM, Richard Damon wrote:
>>> On 3/1/25 8:22 PM, olcott wrote:
>>>> On 3/1/2025 3:58 PM, Richard Damon wrote:
>>>>> On 2/28/25 6:57 PM, olcott wrote:
>>>>>> On 2/28/2025 8:30 AM, Richard Damon wrote:
>>>>>>> On 2/27/25 11:02 PM, olcott wrote:
>>>>>>>> On 2/27/2025 7:00 PM, Richard Damon wrote:
>>>>>>>>> On 2/27/25 9:46 AM, olcott wrote:
>>>>>>>>>> On 2/27/2025 6:45 AM, Richard Damon wrote:
>>>>>>>>>>> On 2/26/25 11:24 PM, olcott wrote:
>>>>>>>>>>>> On 2/26/2025 9:59 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 2/26/25 8:39 PM, olcott wrote:
>>>>>>>>>>>>>> On 2/26/2025 10:03 AM, joes wrote:
>>>>>>>>>>>>>>> Am Wed, 26 Feb 2025 08:34:47 -0600 schrieb olcott:
>>>>>>>>>>>>>>>> On 2/26/2025 6:18 AM, joes wrote:
>>>>>>>>>>>>>>>>> Am Tue, 25 Feb 2025 12:40:04 -0600 schrieb olcott:
>>>>>>>>>>>>>>>>>> On 2/25/2025 12:15 PM, joes wrote:
>>>>>>>>>>>>>>>>>>> Am Mon, 24 Feb 2025 20:02:49 -0600 schrieb olcott:
>>>>>>>>>>>>>>>>>>>> On 2/24/2025 6:12 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>> On 2/24/25 6:11 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>> On 2/24/2025 6:27 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 2/23/25 11:39 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 2/23/2025 8:50 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> On 2/23/25 1:08 PM, olcott wrote:
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> Sure I do.
>>>>>>>>>>>>>>>>>>>>>>> A Systems is semantically sound if every 
>>>>>>>>>>>>>>>>>>>>>>> statement that can be
>>>>>>>>>>>>>>>>>>>>>>> proven is actually true by the systems semantics,
>>>>>>>>>>>>>>>>>>>>>> That is very good.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> in other words, the system doesn't allow the 
>>>>>>>>>>>>>>>>>>>>>>> proving of a false
>>>>>>>>>>>>>>>>>>>>>>> statement.
>>>>>>>>>>>>>>>>>>>>>> That is not too bad yet ignores that some 
>>>>>>>>>>>>>>>>>>>>>> expressions might not
>>>>>>>>>>>>>>>>>>>>>> have any truth value.
>>>>>>>>>>>>>>>>>>>>> Which has nothing to do with "soundness".
>>>>>>>>>>>>>>>>>>>> When any system assumes that every expression is 
>>>>>>>>>>>>>>>>>>>> true or false and
>>>>>>>>>>>>>>>>>>>> is capable of encoding expressions that are neither 
>>>>>>>>>>>>>>>>>>>> IT IS STUPIDLY
>>>>>>>>>>>>>>>>>>>> WRONG.
>>>>>>>>>>>>>>>>>>> In honour of Gödel this is usually called "incomplete".
>>>>>>>>>>>>>>>>>> Where "incomplete" has always been an idiom for stupid 
>>>>>>>>>>>>>>>>>> wrong.
>>>>>>>>>>>>>>>>> Your understanding of logic is incomplete.
>>>>>>>>>>>>>>> Which is to say, stupidly wrong.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> The screwed up notion of "incomplete" is anchored in the 
>>>>>>>>>>>>>>>> stupid idea
>>>>>>>>>>>>>>>> that {true in the system} is not required to be 
>>>>>>>>>>>>>>>> {provable in the
>>>>>>>>>>>>>>>> system}.
>>>>>>>>>>>>>>> You are about a century behind on the foundations of 
>>>>>>>>>>>>>>> mathematics.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Any expression of language that can only be verified as 
>>>>>>>>>>>>>>>> true on the
>>>>>>>>>>>>>>>> basis of other expressions of language either has a 
>>>>>>>>>>>>>>>> semantic connection
>>>>>>>>>>>>>>>> truthmaker to these other expressions or IT IS SIMPLY 
>>>>>>>>>>>>>>>> NOT TRUE.
>>>>>>>>>>>>>>> I.e. its negation is true.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> WTF is the truth value of the negation of nonsense?
>>>>>>>>>>>>>> The Liar Paradox has ALWAYS simply been nonsense.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> But we aren't negating "nonsense", we are negating the 
>>>>>>>>>>>>> actual valid truth value out of the Truth Primative.
>>>>>>>>>>>>>
>>>>>>>>>>>>> You don't seem to understand that the DEFINITION of what a 
>>>>>>>>>>>>> truth primative is requires that True(Nonsense) be false, 
>>>>>>>>>>>>> not "nonsense".
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>   True("lkekngnkerkn") == false
>>>>>>>>>>>> False("lkekngnkerkn") == false
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> But ~True("lkekngnkerkn") == true.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Yes
>>>>>>>>>>
>>>>>>>>>>> so if we can define that lkekngnkerkn is ~True(lkekngnkerkn) 
>>>>>>>>>>> then we have a problem.
>>>>>>>>>>> f
>>>>>>>>>>
>>>>>>>>>> We are not defining gibberish as anything.
>>>>>>>>>> Gibberish evaluates as ~True because it is gibberish.
>>>>>>>>>
>>>>>>>>> But you are trying to define LP := !True(LP) as gibberish.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Prolog already knows that it <is> gibberish.
>>>>>>>
>>>>>>> Because, like you, Prolog can't handle the needed logic.
>>>>>>>
>>>>>>>>
>>>>>>>> It has an infinite cycle in the directed graph of its
>>>>>>>> evaluation sequence.
>>>>>>>
>>>>>>> But infinite cycles are not prohibited in logic systems that 
>>>>>>> support the properties of the Natural Numbers. The MUST allow 
>>>>>>> them or you can't HAVE the Natural Numbers.
>>>>>>>
>>>>>>>>
>>>>>>>> See Page 3 for Prolog
>>>>>>>> https://www.researchgate.net/ 
>>>>>>>> publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
>>>>>>>>
>>>>>>>
>>>>>>> Just shows your stupidity, thinking that all logic is just 
>>>>>>> primitive, and not understanding what the Godel sentence actually 
>>>>>>> is. Your mind seems to have blocked out the actual sentence 
>>>>>>> presented earlier because you know you don't understand it, so 
>>>>>>> you think it must be gibberisn, but it is you mind that is 
>>>>>>> gibberish.
>>>>>>>
>>>>>>> You didn't give it the ACTUAL Godel sentence, just the simplified 
>>>>>>> interpretation of it. The problem is that the actual Godel 
>>>>>>> sentence can't be expressed in Prolog, as it uses 2nd order logic 
>>>>>>> operations, which Prolog doesn't handle.
>>>>>>>
>>>>>>> Of course, since your mind can't handle them either, you can't 
>>>>>>> understand that.
>>>>>>
>>>>>> Carefully study the Clocksin and Mellish on page 3 knucklehead.
>>>>>> Read and reread the yellow highlighted text until you totally get it.
>>>>>>
>>>>>
>>>>> Right, Neither G nor ~G are provable in F.
>>>>>
>>>>
>>>> Provable(common)
>>>> {shown to be definitely true by whatever means}
>>>> is the only relevant notion of provable.
>>>
>>> And "Shown" requires finite.
>>>
>>> Please show me an infinite proof.
>>>
>>> Try to do it. That might be your task if Gehenna.
>>>
>>>>
>>>> We could say that it is totally impossible for anyone
>>>> to touch their own head by adding the requirement
>>>> that they must touch their own head without ever
>>>> touching their own head.
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